New Results on Perceptual Distortion Minimization and Nonlinear Least-Squares Frequency Estimation

In a paper in this journal, a framework was presented wherein a number of practical methods for finding the perceptually most important sinusoids in audio signals could be related using a particular perceptually motivated distortion measure, and it was argued that for Gaussian noise and a large number of samples, these methods should attain the Cramér-Rao lower bound. In this correspondence, we report some new results on this subject. Specifically, we analyze the finite-sample performance of these methods in experiments, and we conclude that for a high number of samples, they perform close to the Cramér-Rao lower bound. However, for a low number of observations, we demonstrate that special care must be taken in designing the perceptually motivated distortion measure if high-resolution estimates are desired. In particular, the smoothness of the frequency response of the perceptual filter that implements the distortion measure is shown to be important.